The question of how North Korea will respond to the death of former first lady Lee Hee-ho, who along with her late husband, President Kim Dae-jung, devoted her life to improving inter-Korean relations, is the focus of attention as Pyongyang has been lukewarm for months toward Seoul’s offers of cross-border cooperation.

The Unification Ministry said Tuesday it had delivered the news of Lee’s death to the North in the morning through the inter-Korean liaison office in the North’s border town of Kaesong at the request of the funeral committee.

Former South Korean president Kim Dae-jung (left) poses with late North Korean leader Kim Jung-il (center) and his wife Lee Hee-ho on his arrival in the North's capital, Pyongyang, June 13, 2000. (Yonhap)

In the past, North Korea has dispatched high-level delegations to the South when a person who contributed greatly to the improvement of relations between the two Koreas died.

Among them has been Lee’s husband Kim, who won the Nobel Peace Prize in 2000 for his efforts to engage with the North, as well as late Hyundai Group founder Chung Ju-yung, who played a key role in laying the groundwork for inter-Korean economic cooperation.

Pyongyang had not responded to Lee’s death as of 5 p.m. Tuesday.

Kim Sung-jae, the director of the Kim Dae Jung Peace Center, said no one from North Korea had contacted him about attending the funeral.

“It is inappropriate for the authorities to predict the possibility of a (North Korean) delegation’s visit,” a Unification Ministry official said.

The former first lady traveled to Pyongyang on Dec. 26, 2011, for the funeral of Kim Jong-il, the current leader’s father. During that visit she met Kim Jong-un, becoming the first South Korean figure to see him after he succeeded his father.

When former President Kim Dae-jung passed away in August 2009, the North’s response was swift.

One day after Kim’s death on Aug. 18, the North sent a fax to the Kim Dae Jung Peace Center, founded by Kim to promote inter-Korean reconciliation and world peace, notifying it of its plans to send a North Korean delegation to visit the South for the funeral.

The North Korean delegation, which consisted of six senior officials -- including Kim Ki-nam, then-secretary of the Workers’ Party -- spent three days in Seoul, meeting with then-President Lee Myung-bak and Unification Minister Hyun In-taek.

The South Korean government is hoping for a conciliatory gesture from the North to create a breakthrough in inter-Korean relations, which have been stalled since North Korean leader Kim Jong-un’s second summit with US President Donald Trump ended without a deal in February.

“If North Korea decides not to dispatch a delegation and just send condolences in Kim Jong-un’s name, skepticism over Chairman Kim’s willingness to improve the South-North Korea relations will spread rapidly,” said Cheong Seong-chang, vice president of research planning at the Sejong Institute.